Okay, after nearly two years I'm finally getting back to dealing with this problem. I've had two repairmen out. One saw that I had the "iceball" problem and told me I needed to go through GE factory repair to get it fixed. Then today the GE guy came out and noticed that the iceball isn't where most of the water is coming from.

There is a LOT of condensation on the side wall of the refrigerator compartment, around where the temperature sensor is located. He said this is because ice has formed inside the wall between the fridge and freezer. Having the sensor on top of that ice explains why we the temperature of both the fridge and freezer have been off. He also said that there is NO fix for this issue. The ice is mingled in with the blown in insulation, and can't be removed effectively.

Can someone tell me if this sounds right? Do I really need to get a new unit?